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Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

January 28, 2022

K3 Surfaces and the Number 24

Posted by John Baez

I’m seeking an explicit vector field with exactly 24 zeros, each of index 1, on a K3 surface. This sounds sort of dry and boring, but it’s not! Let me explain.

This post will start out with some gentle exposition, and then lead to an open question that’s been bothering me. If you’re a beginner, start at the beginning. If you’re an expert, maybe start at the end.

Continue reading “K3 Surfaces and the Number 24” …
Posted at 8:43 PM UTC | Permalink | Followups (26)

January 26, 2022

Learning Computer Science With Categories

Posted by John Baez

The first book in Bob Coecke’s series on applied category theory is out, and the pdf is free — legally, even! — until 8 February 2022. Grab a copy now:

Continue reading “Learning Computer Science With Categories” …
Posted at 6:07 PM UTC | Permalink | Followups (3)

January 25, 2022

Categories in Chemistry, Computing, and Social Networks

Posted by John Baez

This article does two things:

It urges you — or your friends, or students — to apply for our free summer school in applied category theory run by the American Mathematical Society. It’s also a quick intro to some key ideas in applied category theory!

Applications are due Tuesday 2022 February 15 at 11:59 Eastern Time — go here for details. If you get in, you’ll get an all-expenses-paid trip to a conference center in upstate New York for a week in the summer. There will be a pool, bocci, lakes with canoes, woods to hike around in, campfires at night… and also whiteboards, meeting rooms, and coffee available 24 hours a day.

You can work with me on categories in chemistry, Nina on categories in the study of social networks, or Valeria on categories applied to concepts from computer science, like lenses.

Continue reading “Categories in Chemistry, Computing, and Social Networks” …
Posted at 10:13 PM UTC | Permalink | Post a Comment

January 7, 2022

Optimal Transport and Enriched Categories IV: Examples of Kan-type Centres

Posted by Simon Willerton

Last time we were thinking about categories enriched over ℝ¯ +\bar{\mathbb{R}}_+, the extended non-negative reals; such enriched categories are sometimes called generalized or Lawvere metric spaces. In the context of optimal transport with cost matrix kk, thought of as a ℝ¯ +\bar{\mathbb{R}}_+-profunctor k:𝒮⇝ℛk\colon \mathcal{S}\rightsquigarrow\mathcal{R} between suppliers and receivers, we were interested in the centre of the ‘Kan-type adjunction’ between enriched functor categories, which is the following:

In this post I want to give some examples of the Kan-type centre in low dimension to try to give a sense of what they look like over ℝ¯ +\bar{\mathbb{R}}_+. Here’s the simplest kind of example we will see.

kan_centre_32.png

Continue reading “Optimal Transport and Enriched Categories IV: Examples of Kan-type Centres” …
Posted at 1:55 PM UTC | Permalink | Post a Comment

Intercats

Posted by John Baez

The Topos Institute has a new seminar:

The talks will be streamed and also recorded on YouTube.

It’s a new seminar series on the mathematics of interacting systems, their composition, and their behavior. Split in equal parts theory and applications, we are particularly interested in category-theoretic tools to make sense of information-processing or adaptive systems, or those that stand in a ‘bidirectional’ relationship to some environment. We aim to bring together researchers from different communities, who may already be using similar-but-different tools, in order to improve our own interaction.

Continue reading “Intercats” …
Posted at 5:55 AM UTC | Permalink | Post a Comment

January 2, 2022

Adjoint School 2022

Posted by John Baez

Every year since 2018 we’ve been having annual courses on applied category theory where you can do research with experts. It’s called the Adjoint School.

You can apply to be a student at the 2022 Adjoint School now, and applications are due January 29th! Go here:

Read on for more about how this works!

Continue reading “Adjoint School 2022” …
Posted at 6:20 AM UTC | Permalink | Followups (2)